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Answer: There is a short position in an S&P 500 futures contract that will make his portfolio insensitive to both small and large moves in the S&P 500.
## Explanation Let's analyze each statement: **A. He can make his portfolio delta neutral by shorting index futures contracts.** - **CORRECT** - When writing a put option, the position has positive delta (since put options have negative delta, and writing them creates positive delta exposure) - Shorting index futures (which have delta = -1) can offset this delta exposure **B. There is a short position in an S&P 500 futures contract that will make his portfolio insensitive to both small and large moves in the S&P 500.** - **INCORRECT** - Futures contracts only provide delta hedging (first-order sensitivity) - They do not hedge gamma risk (second-order sensitivity to large price moves) - The portfolio would still be sensitive to large price movements due to gamma exposure **C. A long position in a traded option on the S&P 500 will help hedge the volatility risk of the option he has written.** - **CORRECT** - Options have vega exposure (sensitivity to volatility) - A long position in another option can offset the vega risk from the written put **D. To make his hedged portfolio gamma neutral, he needs to take positions in options as well as futures.** - **CORRECT** - Futures have zero gamma (linear instruments) - Only options have gamma exposure - To hedge gamma, positions in other options are necessary Therefore, statement **B** is not correct.
Author: LeetQuiz Editorial Team
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Mr. Black has been asked by a client to write a large put option on the S&P 500 index. The option has an exercise price and a maturity that is not available for options traded on exchanges. He, therefore, has to hedge the position dynamically. Which of the following statements about the risk of his position are not correct?
A
He can make his portfolio delta neutral by shorting index futures contracts.
B
There is a short position in an S&P 500 futures contract that will make his portfolio insensitive to both small and large moves in the S&P 500.
C
A long position in a traded option on the S&P 500 will help hedge the volatility risk of the option he has written.
D
To make his hedged portfolio gamma neutral, he needs to take positions in options as well as futures.
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